The activity of a radioactive sample falls from \(700 \;\mathrm{s}^{-1}\) to \(500\; \mathrm{s}^{-1}\) in \(30\;min\). Its half life is close to.........\(min\)

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

Two identical cells each of emf \(1.5\,V\) are connected in series across a \(10\,\Omega\) resistance. An ideal voltmeter connected across \(10\,\Omega\) resistance reads \(1.5\,V\). The internal resistance of each cell is \(......\Omega\).

A cyclist starts from the point \(P\) of a circular ground of radius \(2 \mathrm{~km}\) and travels along its circumference to the point \(\mathrm{S}\). The displacement of a cyclist is _______.

For a certain organ pipe, the first three resonance frequencies are in the ratio of \(1:3:5\) respectively. If the frequency of fifth harmonic is \(405\,Hz\) and the speed of sound in air is \(324 \,ms ^{-1}\) the length of the organ pipe is \(..........m.\)

A bar magnet has total length \(2 l=20\) units and the field point \(P\) is at a distance \(\mathrm{d}=10\) units from the centre of the magnet. If the relative uncertainty of length measurement is \(1 \%\), then uncertainty of the magnetic field at point P is :

One main scale division of a vernier callipers is \(a\) \(cm\) and \(n ^{\text {th }}\) division of the vernier scale coincide with \(( n -1)^{\text {th }}\) division of the main scale. The least count of the callipers in \(mm\) is

An electric field \(\overrightarrow{\mathrm{E}}=(2 \mathrm{xi}) \mathrm{NC}^{-1}\) exists in space. \(\mathrm{A}\) cube of side \(2 \mathrm{~m}\) is placed in the space as per figure given below. The electric flux through the cube is _______ \(\mathrm{Nm}^2 / \mathrm{C}\)

The magnetic field at the centre of a current carrying circular loop of radius \(R\) is 16 \(\mu\)T. The magnetic field at a distance \(x = \sqrt{3}R\) on its axis from the centre is ________ \(\mu\)T.

A thin biconvex lens is prepared from the glass (\(\mu=1.5\)) both curved surfaces of which have equal radii of \(20\) cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ________ cm.

A small soap bubble of radius \(4\,cm\)  is trapped inside another bubble of radius \(6\,cm\) without any contact. Let \(P_2\)  be the pressure inside the inner bubble and \(P_0\)  the pressure outside the outer bubble. Radius of another bubble with pressure difference \(P_2 - P_0\)  between its inside and outside would be....... \(cm\)

The recoil speed of a hydrogen atom after it emits a photon in going from \(n =5\) state to \(n =1\) state will be ..... \(m/s\)

In a single slit diffraction pattern, a light of wavelength \(6000\) A is used. The distance between the first and third minima in the diffraction pattern is found to be \(3 \mathrm{~mm}\) when the screen in placed 50 \(\mathrm{cm}\) away from slits. The width of the slit is _______ \(\times 10^{-4} \mathrm{~m}\).